The 21-year-old, who has represented the Republic of Ireland at youth team level, has impressed his boss since being handed an opportunity in the first team, owing in part to an injury crisis at centre-back.
His current contract expires at the end of this season.
'Surprised' Sheffield Wednesday boss Darren Moore to send Paul Heckingbottom message after Slavisa Jokanovic's Sheffield United sacking
"Ciaran’s done really well coming in,” said Moore.
"He’s got a wonderful appetite for the game. For a young player, every time he’s trained with us he’s always had a wonderful belief about himself.
"In terms of coming into the system that’s he’s come in to, he’s shown, for someone so young, a wonderful maturity about him. I think that’s been the biggest thing I’ve noted with him.
"Going forward, looking at his contractual situation, we’ll see.”
Local lad Brennan was recalled from a loan spell with National League side Notts County earlier this month and went straight into the starting XI for Wednesday’s final Papa John’s Trophy group stage match against Harrogate Town.
He helped the team keep a clean sheet that night and has since started the Owls’ last two league games.
With Dominic Iorfa, Lewis Gibson and temporary stand-in Marvin Johnson all still out, he looks set to continue at the heart of defence against second-placed Wycombe Wanderers on Saturday.
"He’ll want to keep his consistency in his performances going,” Moore said.
"He won’t get sidelined and lose focus. He’s a player here at Sheffield Wednesday we admire a lot.
"He’s got a lot more to learn with his game and he’s learning all the time.”
Sheffield Wednesday lost Liam Shaw and Osaze Urhoghide to Celtic for modest £250,000 development fees this summer after their deals were allowed to run down.
The club has previously seen George Hirst – the son of Owls legend David – and Sean Clare depart in similar circumstances.
Moore has already moved to tie down several of his star players to new contracts this season, including Iorfa, Josh Windass and Liam Palmer.
Discussions have also been held with Callum Paterson over a new deal.